Reports of a fling between the pair began earlier this year, although both Lovato and Horan have vehemently denied the claims.
A source told Celebuzz that the pair were spotted together after the recent MTV Video Music Awards, where Horan's band One Direction won three awards.
The pair were allegedly seen sharing a meal at the Pink Taco restaurant in Century City, California on Thursday night (September 6).
"It looked like a first date," explained the source. "(They were) sharing guacamole and queso as they got to know one another, and kept it really private and low key."
Horan has also sparked a playful flirtation with singer Katy Perry, who he kissed on the VMA stage after winning an award.
Perry later tweeted at him: "I'll be your Mrs. Robinson."
Watch a promo for The X Factor USA, featuring Demi Lovato as a judge, below: